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Abstract

Many common adaptive beamforming methods are based on a sample matrix inversion (SMI). The schemes can be applied in two ways. The sample covariance matrices are either computed over preambles, or the sample basis for the SMI and the target of the beamforming are identical. A vector space representation provides insight into the classic SMI-based beamforming variants, and enables elegant derivations of the well-known second-order statistical properties of the output signals. Moreover, the vector space representation is helpful in the definition of appropriate interfaces between beamfoming and soft-decision signal decoding in receivers aiming at adaptive cochannel interference mitigation. It turns out that the performance of standard receivers incorporating SMI-based beamforming on short signal intervals and decoding of BICM (bit-interleaved coded modulation) signals can be significantly improved by proper interface design.

Introduction

Cochannel interference (CCI) becomes a major performance limiting factor in today's growing variety and density of wireless links and networks. Cellular systems occupying licensed frequency bands may evade CCI by a smart channel reuse policy. But in emerging decentralized peer-to-peer networks an efficient management of the channel access with the guarantee of limited CCI is a complex task, especially if the peers have directional transmission and reception capabilities. And proactive interference control across different systems sharing an unlicensed band is even more difficult to realize. Receiver techniques aiming at reactive interference mitigation, on the other hand, do not require cooperation between transceivers or systems, and they are thus a more viable approach to limit outages in decentralized or heterogeneous networking scenarios.

Data streams are normally split up and conveyed in short frames from sender to receiver. In multi-hop networks the frames need to be lightweight in order to limit latency in links over multiple hops since the relaying peers can usually not receive and transmit simultaneously. Moreover, besides of the data frames a multitude of even shorter control frames conveying “Hello”, “Request/Clear to Transmit”, “Acknowledge” messages and others are exchanged. As a consequence, if a channel is shared without coordination the interference may fluctuate at a much higher rate than the actual channel gain does due to multipath fading. This necessitates interference mitigation techniques which can adapt to CCI characteristics within short signal periods.

Equipped with array antennas, receivers can suppress interference via beamforming, i.e., a weighting and combining of the signals from the multiple antennas. Classic beamforming methods include the minimum variance distortionless response (MVDR) beamformer, which maximizes the signal-to-interference-plus-noise ratio (SINR) under the constraint of undistorted desired signal, and the minimum mean squared error estimator. When the spatial signatures of the interfering signals are completely unknown, an adaptive beamforming becomes necessary. Many of the popular adaptive beamforming techniques, discussed in textbooks like (Monzingo et al, 1980; Van Trees, 2002), rely on an inversion of a sample covariance matrix (SCM). The methods presented in (Vorobyov et al, 2003; Feldman et al, 1994; Bell et al, 2000; Lorenz et al, 2005; Li et al, 2003) feature enhanced robustness to mismatches in the spatial signature of the desired signal and other uncertainties via a diagonal loading of the SCM or more elaborate arrangements. The properties of the output of classic SCM-based spatial filters are analyzed in (Richmond, 1996; Van Veen, 1991), exposing the performance degradation compared to ideal beamforming based on perfectly known CCI statistics.